1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
DENIUS [597]
3 years ago
12

A cannon tilted up at a 29.0° angle fires a cannon ball at 81.0 m/s from atop a 22.0 m -high fortress wall. What is the ball's i

mpact speed on the ground below?

Physics
1 answer:
Sergeu [11.5K]3 years ago
4 0

Answer:

The speed of the ball when it hits the ground is 83.4 m/s

Explanation:

Please see the attached figure for a description of the problem.

The vector velocity at time "t" can be written as follows:

v = (v0 * cos\alpha ; v0 * sin\alpha + g*t)

where:

v0 : module of the initial velocity vector.

α: launching angle.

g: acceleration due to gravity.

t: time

To calculate the impact speed, we can use this equation once we know the time at which the ball hits the ground. For this, we can use the equation for position:

r = ( x0 + v0*t*cos\alpha ; y0 + v0*t*sin\alpha + 1/2 g*t^{2})

where:

r= vector position

x0 = horizontal initial position

y0 = vertical initial position

The problem gives us information about the vertical displacement. If we take the base of the wall as the center of the reference system, at the time at which the ball hits the ground, the module of the vertical component of the vector position, r, is 0 m (see figure). The initial vertical position is  22 m.

if ry is the vertical component of the vector r at final time:

ry = (0; y0 + v0*t*sin\alpha +1/2 g*t^{2})

then, the module of ry is (see figure):

module ry =0 = 22m + v0*t*sin\alpha + 1/2*g*t^{2}

Let´s replace with the given data:

0 = 22m + 39.3 m/s*t -4.9 m/s^{2}*t^{2}

Solving the quadratic equation:

t = -0.5 and t = 8.5 s

At 8.5 s after firing, the ball hits the ground.

Now, we can find the module of the velocity vector when the ball hits the ground:

v = (v0 * cos\alpha ; v0 * sin\alpha + g*t)

at time t = 8.5s

v = (81.0m/s * cos\alpha ; 81.0m/s * sin\alpha - 9.8 m/s^{2} *8.5s)

v = (70.8 m/s; -44.0 m/s)

module of v = \sqrt{(70.8m/s)^{2} + (-44.0m/s)^{2}} = <u>83.4 m/s</u>

You might be interested in
If the period of a spring is 5 seconds what is the frequency
Scilla [17]

Answer:

C. 0.2 Hertz

Explanation:

The frequency of a spring is equal to the reciprocal of the period:

f=\frac{1}{T}

where

f is the frequency

T is the period

For the spring in this problem,

T = 5 s

therefore, the frequency is

f=\frac{1}{5 s}=0.2 Hz

7 0
3 years ago
A wave hits a wall as shown. As the wave interacts with a wall, which kind of wave interaction is shown? absorption diffraction
dangina [55]
The answer is reflection.

The drawing is simple but illustrates the concept beautifully.
8 0
3 years ago
Read 2 more answers
. A toy rocket has a mass of 350 g at launch. The force it produces
nydimaria [60]

Answer:

the acceleration is reduced by gravity

a = (15 / .35) - [9.8 * sin(65º)]

Explanation:

break the launch vector into two components, vertical and horizontal

Force Net Vertical=-9.8*.350+15cos65 N

force net horizonal=15sin65

initial acceleration= force/mass= (-9.8+15/.350*cos65)j+(15/.350*sin65)i

using i,j vectors..

5 0
3 years ago
answers At the beginning of 2019, Robotics Inc. acquired a manufacturing facility for $12.3 million. $9.3 million of the purchas
pshichka [43]

Answer:

$613,077

Explanation:

Calculation for the depreciation on the building for 2021

First step is to calculate the depreciation expense for the year 2019 and 2020 using this formula

Depreciation expense = (Purchase price - Residual value) ÷ (Useful life)

Let plug in the formula

Depreciation expense= ($9,300,000 - $1,300,000) ÷ (20 years)

Depreciation expense= ($8,000,000) ÷ (20 years)

Depreciation expense= $400,000

Second step is to calculate the book value for the year 2021 using this formula

Book value = Purchase price - Depreciation expenses *2 years

Let plug in the formula

Book value= $9,300,000 - $400,000 × 2

Book value= $8,500,000

Last step is to calculate the depreciation for 2021 using this formula

2021 Depreciation=(Book value-Residual value)÷Useful life

2021 Depreciation= ($8,500,000 - $530,000) ÷ (15 years - 2 years)

2021 Depreciation=$7,970,000÷13 years

2021 Depreciation= $613,077

Therefore the depreciation on the building for 2021 will be $613,077

8 0
2 years ago
Which describes the greatest amount of ice cream?
solmaris [256]

We must know that the gravity acceleration on Jupyter is g = 24.79 m/s² , on the Earth g = 9.8 m/s² and on the moon 1.62 m/s².

The weigh of an object is given by:

P = mg

Solving for m:

m = P/g

We see that for the same weight, if gravity is less, then the amount of mass is greater, because they are inversely proportional. So we conclude that the answer is:

<h2>a 3-N bowl of ice cream on the moon </h2>
8 0
2 years ago
Other questions:
  • A 20000 kg railroad car is rolling at 1.00 m/s when a 1000 kg load of gravel is suddenly dropped in. part a what is the car's sp
    9·1 answer
  • The allowed energies of a simple atom are 0.0 eV, 3.0 eV, and 4.0 eV. An electron traveling at a speed of 1.3*10^6 m/s collision
    5·1 answer
  • A wave has a wavelength of 6 mm and a frequency of 9 hertz. What is its speed? what is the answer and units?
    15·1 answer
  • Existing rocks can become sedimentary rocks when they are subjected to which conditions?
    6·1 answer
  • A mass attached to a 50.0 cm long string starts from rest and is rotated 40 times in one minute before reaching a final angular
    6·1 answer
  • A water pump with a power of 3.4 × 102 watts lifts water at the rate of 7.5 × 10-2 meters/second from a water tank. What is the
    8·1 answer
  • A projectile is launched with an initial velocity of 60.0 m/s at an angle of 30.0° above the horizontal. How far does it travel?
    12·2 answers
  • BRAINLIEST, PLEASE pls pls pls pls pls pls pls pls pls pls pls plsl plsssssssssssssssssssssssssssssssssssssssssssssssssssssssss
    13·1 answer
  • Where does the majority of the mass of an atom come from
    7·2 answers
  • How many electrons should be in an atom’s valence shell (with the exception of hydrogen and helium) to become stable? 2 4 6 8.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!